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2\left(x-1\right)-3\left(x+1\right)=6
Multiply both sides of the equation by 6, the least common multiple of 3,2.
2x-2-3\left(x+1\right)=6
Use the distributive property to multiply 2 by x-1.
2x-2-3x-3=6
Use the distributive property to multiply -3 by x+1.
-x-2-3=6
Combine 2x and -3x to get -x.
-x-5=6
Subtract 3 from -2 to get -5.
-x=6+5
Add 5 to both sides.
-x=11
Add 6 and 5 to get 11.
x=-11
Multiply both sides by -1.